%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV131+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:06:52 AM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 4 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 26 ( 8 avg)
% Number of connectives : 68 ( 17 ~; 1 |; 24 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(gauss_array_0001,conjecture,
( ( ( gt(loopcounter,n0)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ~ leq(tptp_float_0_001,pv1341) )
=> leq(n0,s_best7) ),
file('theBenchmark.p',gauss_array_0001) ).
fof(gauss_array_0001_neg,negated_conjecture,
~ ( ( ( gt(loopcounter,n0)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ~ leq(tptp_float_0_001,pv1341) )
=> leq(n0,s_best7) ),
inference(assume_negation,[status(cth)],[gauss_array_0001]) ).
cnf(c_367,negated_conjecture,
~ leq(tptp_float_0_001,pv1341),
inference(clausify,[status(thm)],[gauss_array_0001_neg]) ).
cnf(c_368,negated_conjecture,
( leq(n0,s_best7)
| leq(tptp_float_0_001,pv1341) ),
inference(clausify,[status(thm)],[gauss_array_0001_neg]) ).
cnf(c_369,negated_conjecture,
leq(n0,s_best7),
inference(resolve,[status(thm)],[c_367,c_368]) ).
cnf(c_380,negated_conjecture,
~ leq(n0,s_best7),
inference(clausify,[status(thm)],[gauss_array_0001_neg]) ).
cnf(c_381,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_369,c_380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV131+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 13:10:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 792505 was started by sandbox2 on n017,
% 0.11/0.37 % Sat Sep 26 13:10:48 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.43
% 0.11/0.43 % From the command line: assign(max_seconds, 300).
% 0.19/0.50
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50
% 0.19/0.50 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.19/0.50 % Length of proof is 6.
% 0.19/0.50 % Level of proof is 3.
% 0.19/0.50 % Maximum clause weight is 8.000.
% 0.19/0.50 % Given clauses 0.
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------